Splitting of energy of dispersive waves in a star-shaped network

We study wave and Klein-Gordon equations in a star-shaped network. In the wave case we state a d'Alembert-type solution formula generalizing the formula obtained in Ali Mehmeti [1] and [4] for four branches. In the Klein-Gordon case (dispersive waves) we solve the problem using the Laplace transform with respect to time. We state a continuity equation linking the energy density and the energy flow for the Klein-Gordon equation in a star-shaped network. We observe that the splitting of energy at the central node is the same for propagating waves with and without dispersion.